Find the domain of the real-valued function
f(x) = -sqrt(-10x^2 - 4x + 6)
Give the endpoints in your answer as common fractions, not mixed numbers or decimals.
+128474 f(x) = - sqrt ( -10x^2 - 4x + 6)
We must have that
-10x^2 - 4x + 6 ≥ 0 multiply through by -1 and reverse the inequality sign
10x^2 + 4x - 6 ≤ 0 factor as
(10x - 6) ( x + 1) ≤ 0 (1)
10x - 6 = 0 x + 1 = 0
10x = 6 x = -1
x = 6/10 = 3/5
We have three intervals to consider (-inf, -1] , [ -1, 3/5 ] , [ 3/5, +inf )
The midle interval is the one that makes (1) true
So.....the domain is [ -1, 3/5 ]
See the graph here : https://www.desmos.com/calculator/xwiv35snre
